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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Experimental polarization state tomography using photon counting polarimeters

Alexander Ling, Kee Pang Soh, Antı́a Lamas-Linares, Christian Kurtsiefer

Published Aug 31, 2006• 0 citations
Publisher

Abstract

We report on the implementation of a photon counting polarimeter based on a scheme known to be optimal for obtaining the polarization vector of ensembles of spin-1/2 quantum systems. We show how to use this polarimeter to estimate the complete polarization state for generic multi-photon states. State reconstruction using the polarimeter is illustrated by actual measurements on prepared ensembles of one- and two-photon systems. The rate at which the estimated polarization state converges to an asymptote state is also measured and presented.

DOI
10.1117/12.678921

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We report on the implementation of a photon counting polarimeter based on a scheme known to be optimal for obtaining the polarization vector of ensembles of spin-1/2 quantum systems. We show how to use this polarimeter to estimate the complete polarization state for generic multi-photon states. State reconstruction using the polarimeter is illustrated by actual measurements on prepared ensembles of one- and two-photon systems. The rate at which the estimated polarization state converges to an asymptote state is also measured and presented.
We report on the experimental implementation of a polarimeter based on a scheme known to be optimal for obtaining the polarization vector of ensembles of spin-12\frac{1}{2}21​ quantum systems and the alignment procedure for this polarimeter. We also show how to use this polarimeter to estimate the polarization state for identically prepared ensembles of single photons and photon pairs and extend the method to obtain the density matrix for generic multiphoton states. State reconstruction and performance of the polarimeter is illustrated by actual measurements on identically prepared ensembles of single photons and polarization entangled photon pairs.
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A continuous positive operator-valued measurement (POVM) is described for the polarization state of a single photon propagating in a known spatiotemporal mode. This POVM is shown to be the maximum-likelihood quantum measurement for estimating that polarization state. Moreover, the maximum-likelihood polarization estimate derived from this POVM enables uniformly optimal measure-and-prepare state transmission via classical communication---at the F‾=2/3\overline{F}=2/3F=2/3 classical limit on average teleportation fidelity---for any pure state of polarization. When two continuous-POVM polarimeters are used to detect the singlet state of a pair photons that are in distinct spatial modes, the conditional probability density for one polarimeter's output given the other's encompasses the quantum interference patterns seen in standard singlet-state polarization analysis. For single-photon illumination, a 1:M1:M1:M optical splitter followed by a collection of MMM projective polarization measurements, whose bases are uniformly distributed over the Poincar\'e sphere, yields observation statistics that converge in distribution to those of the continuous-POVM polarimeter as $M\ensuremath{\rightarrow}\ensuremath{\infty}$.
We propose a technique for performing quantum state tomography of photonic polarization-encoded multiqubit states. Our method uses a single rotating wave plate, a polarizing beam splitter, and two photon-counting detectors per photon mode. As the wave plate rotates, the photon counters measure a pseudocontinuous signal which is then Fourier transformed. The density matrix of the state is reconstructed using the relationship between the Fourier coefficients of the signal and the Stokes' parameters that represent the state. The experimental complexity, i.e., different wave plate rotation frequencies, scales linearly with the number of qubits.